### Andrew Mathas

University of Sydney

### Elementary divisors of Specht modules

**Friday 19th March, 12:05-12:55pm,
Carslaw 373. **
Let *H* be the Iwahori-Hecke algebra of the symmetric group; this is a
"deformation" of the group algebra of the symmetric group which arises
naturally in the representation theory of the (finite) general linear
groups. If *H* is semisimple, then its irreducible representations are
known as the Specht modules. In the non-semisimple case each irreducible
representation arises as the quotient of some Specht module by its radical.

The Specht modules of *H* come equipped with a natural bilinear form and
one can use this form to define a Gram matrix for the Specht module
(relative to some fixed basis). In this talk we will explain what is
known about the elementary divisors of these Gram matrices, including
giving a beautiful connection between the elementary divisors of a
Specht module and its dual.

This is joint work with Matthias Kuenzer (Ulm).